# linear equations help

#### daniel123

Could anyone help me work out these simultaneous equations, i am really struggling.

A)
3p+q=5
p+3q=-1

B)
7y-9x-13=0
5y-8x-14=0

C)
3.2a -0.7b -0.47 = 0
2.4a +0.35b -0.265 = 0

D)
3r-2t=-0.2
r+s=2.4
4s-t=7.3

E)
i1 + i2 + i3 = 0
50 i1 + 30 i2 = 16
-20 i2 + 5 i3 = -6

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#### bondesan

daniel123,

These are simple system of equations. How did you started it? Show us what you've done. Maybe you should try a few methods of solution to find one that fits well to you - Gaussin elimination, substitution, Cramer's rule, for example.

#### yeKciM

u can use substitution in those simple equation but as u move to bigger systems of equations it could get a little a bit of messy

A) u can multiply second equation with (-3) and add it to the first ... so u'll get q ... after that just put q in any of those starting equations and get p...
or u can say $$\displaystyle q=5-3p$$ that's from first one and put that q in second and solve... or any another way...

that way u can do all of your systems of equations

or u can look at it as determinants and solve that way ... (don't know are u familiar with that but there's system with complex numbers so i think u are)

#### daniel123

This is the way i have done but still, when i verify the answer, i get the one correct but not the other and i carnt see where im going wrong.
for example, question A:

3p+q=5
P+3q=-1

re-arranged:
q=5-3p

substittuted for q:
p + 3(5-3p) = -1
= p + 15 - 9p = -1
= 8p + 15 = -1
= 8p = -16
p=-2

Substittuted for p:
q= 5 - 3(-2)
= 5 - -6
q = 11

VERIFY:
3(-2) + 11
= -6 + 11
= 5 CORRECT

-2 + 3(11)
= -2 + 33
= 31 WRONG

#### yeKciM

$$\displaystyle p=2 , q=-1$$

u have typo mistake $$\displaystyle -8p=-16$$ ... not like you wrote

so $$\displaystyle p=2$$ not $$\displaystyle p=-2$$ and rest will be fine

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daniel123

#### daniel123

ok so im probably going to have to go through these one at a time, as im getting in-sufficent numbers

B)
7y - 9x - 13 = 0
5y - 8x - 12 = 0

So... here we go

35y - 56x - 98) - (35y - 45x - 65)
= 35y - 56x - 98 - 35y + 45x + 65
= -11x - 35
-11x - 35 = 0
-11x = 35
x = -3.18

substittuting for x

7y - 9x (-3.18) - 13 = 0
= 7y + -9.54 - 13 = 0
= 7y + 22.54 = 0
7y = 22.54
y = 3.22

x= -3.18 y=3.22

VERIFIED:
7(3.22) - 9(3.18) - 13 = 0 WRONG

5(3.22) - 8(-3.18) - 14 = 0 WRONG

#### yeKciM

wait... what did u do there...

first equation multiply with let's say 5 , and second one with (-7) ... then u'll get

$$\displaystyle 35y-45x=65$$

$$\displaystyle -35y+56x=-98$$

now add first to second (sum) and then u get x, ... u know the rest

P.S. in your first post free member's are not the same as here ?

#### yeKciM

B)

$$\displaystyle y=-2 \;; x=-3$$

C)

$$\displaystyle a= 0.125 \;; b=-0.1$$

D)

$$\displaystyle r = 0.4 \;; t = 0.7\; ; s= 2$$

E)

$$\displaystyle i_1=0.2 \;; i_2=0.2\;; i_3=-0.4$$

daniel123